A sufficient condition for the fiber of the tangent bundle of a scheme and its Zariski tangent space to be isomorphic

TL;DR

This paper establishes a simple necessary condition under which the Zariski and Grothendieck relative tangent spaces of a scheme are isomorphic, clarifying their relationship in algebraic geometry.

Contribution

It provides a new, straightforward criterion for the isomorphism of Zariski and Grothendieck tangent spaces, enhancing understanding of tangent bundle fibers.

Findings

Identifies a necessary condition for tangent space isomorphism

Clarifies the relationship between Zariski and Grothendieck tangent spaces

Simplifies criteria for tangent space analysis in schemes

Abstract

In this note, we give a simple necessary condition for the Zariski relative tangent space and the Grothendieck relative tangent space to be isomorphic.